Abstract : The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $\partial t u - \Delta u + | abla u|^q = 0$ is investigated for the critical exponent q=N+2-N+1. Convergence towards a rescaled self-similar solution to the linear heat equation is shown, the rescaling factor being $\ln{t}^{-N+1}$. The proof relies on the construction of a one-dimensional invariant manifold for a suitable truncation of the equation written in self-similar variables.